Notation

I= number of projects available for selection;

= the decision vector;

= net present value of project I ;

= initial outlay of project I ;

C= initial available capital;

Fixcharge Positive Function is defined as follows:

Optimization Problem 1

Maximizing net present value

subject to

Constraint on available initial capital

Bounds on positions  

 

Optimization Problem 2

Maximizing net present value

subject to

Constraint on available initial capital

Bounds on positions  

 

It can be proved that the optimal solution of the optimization problem2 is binary, i.e. all components of the optimal vector are equal to 0 or 1.

Initial Data

Number of projects available for selection: I=7.